A ten-year numerical hindcast of hydrodynamics and sediment dynamics in the Loire Estuary

A numerical hindcast of the macrotidal Loire Estuary (France) has been generated to provide a long-term dataset (2008–2018) of estuarine hydrodynamics, temperature, salinity, and sediment dynamics. This hindcast is based on simulations coupling water motion, wave and mixed sediment models, forced with realistic conditions and extensively validated in the salinity gradient and turbidity maximum areas. These data represent extremely valuable information for diverse scientific communities, providing (i) environmental parameters for ecosystemic studies along the Loire River–sea continuum, (ii) a singular estuarine configuration for inter-comparison of estuarine functioning, and (iii) a ten-year synoptical view of a major estuarine environment of the North Atlantic Ocean.

Hydrodynamic model. The model is based on a non-nested (i.e., unique) configuration using the hydrostatic model MARS3D 34 . An orthogonal curvilinear grid is used to better represent the estuarine shape and to optimize computational costs while refining the grid resolution in some specific areas (i.e., in the river meanders, in the central estuary, and at the estuarine mouth; Fig. 1). Horizontal cell size ranges from around 50 m in the meanders to approximately 1.3 km offshore while the vertical grid is divided into 10 equidistant sigma layers.
The 114 main tidal components, extracted from the CST France database, https://maree.shom.fr (Service Hydrographique et Océanographique de la Marine, SHOM), are used to force the circulation at the open boundaries. Surges, provided by a configuration of the two-dimensional MARS2D model applied to a larger domain (i.e., over the Bay of Biscay), are added to the water elevation at these same boundaries. Realistic freshwater discharges and sediment loads are prescribed at the upstream boundary of the Loire River (i.e., Saint Florent-le-Vieil) and at the Vilaine Estuary mouth for the Vilaine River (see further details on river supplies in the "Data records" section). In addition, the model is forced by wind stresses and pressure gradients obtained from the high-resolution meteorological AROME model (Météo-France): https://donneespubliques.meteofrance.fr. The simulated turbulence is based on a k-ε turbulence closure scheme. Waves are simulated with the WAVEWATCH III ® (WW3) numerical model 35 using the same computational grid as the one used by MARS3D in this study. The hourly free surface elevation and current velocity provided by the MARS3D hydrodynamic model, along with local winds and swell data extracted from a larger model, were used to force the WW3 configuration. However, the wave effects on hydrodynamic circulation are not taken into account because of the dominance of tidal currents over wave-induced currents. The bottom orbital velocities simulated by the wave model were used to compute the wave-induced bed shear stress. Finally, the total bed shear stress (τ) was expressed as a combination of the current-induced and wave-induced bed shear stresses, accounting for non-linear interactions following the formulation of Soulsby 36 .
The hydrodynamic bottom roughness z 0b is spatially distributed according to the observed sediment substrate. However, the sediment nature in the estuary changes according to the ETM location and the presence of fluid mud layers, which depend on the Loire River discharge. Therefore, following an approach adopted by ARTELIA 37 , the bottom roughness also depends on the Loire River discharge 38 . More details on the hydrodynamic model configuration are provided by Khojasteh Pour Fard 39 . www.nature.com/scientificdata www.nature.com/scientificdata/ Sediment transport model. The hydrodynamic model is coupled with the process-based, multiclass, multilayer sediment transport model MUSTANG [40][41][42] , which computes the temporal and spatial variations of sand and mud content in the bed under hydrodynamic forces and consolidation process. The MARS3D-MUSTANG coupling resolves advection-diffusion equations in the water column and sediment exchanges between the bed and the water column for different particle classes. Based on hundreds of granulometric samples collected in the Loire Estuary 43 , five sediment classes are prescribed in this hindcast: one mud, three sands, and one gravel (see sediment class diameters in Table 1). Sediment classes are initially distributed according to bed substrate observations from the SHOM. www.nature.com/scientificdata www.nature.com/scientificdata/ Non-cohesive sediment classes (sands and gravel) have constant settling velocities depending on their diameters 36 . The coarser classes are transported in the bottom layer only, except for the very fine sand, which was treated in three dimensions. In two dimensions, the velocity in the bottom layer is corrected to account for a logarithmic profile for the velocity in the whole water column, and the calculated sand concentration is then assumed to follow a Rouse profile 44 . The mud class is computed as a three-dimensional variable with a settling velocity w s,mud varying with concentration and turbulence to represent flocculation processes following van Leussen 45 : with C mud the mud concentration (kg/m 3 ), G the turbulent shear rate (s −1 ), and w s,min , w s,max , a, b, c 1, c 2 calibration parameters detailed in Table 1. A dependency between the mud settling velocity and salinity (S) is also considered to account for the influence of salinity on flocculation 46 : below a critical salinity of 5 psu, the mud settling velocity decreases with salinity (see details in Diaz, et al. 21 ). The erosion flux is based on Partheniades-Arathurai equation 47 : www.nature.com/scientificdata www.nature.com/scientificdata/  36 , the erosion rate is derived from erodibility measurements 48 , and the calibration parameter n is defined as n sand (Table 1).
In the presence of a cohesive seabed (f m > 0.7; Le Hir, et al. 41 ), the formulation follows a pure mud erosion regime with n = n mud and E = E 0,mud ( Table 1). The critical shear stress for mud erosion τ ce,mud depends on the bed consolidation state, which is represented by the relative mud concentration (C relmud ) through a classical www.nature.com/scientificdata www.nature.com/scientificdata/ power law τ ce,mud = α 1 .C relmud α2 (see Grasso,et al. 40 ), with α 1 and α 2 defined in Table 1. Here, C relmud is defined as the mud concentration in the space between sand particles 49 . Finally, for a mixed erosion regime, the erosion law parameters are linearly interpolated between pure sand and pure mud behaviours. The main empirical parameters are identified in Table 1 and further details on the formulations used in this model can be found in Grasso, et al. 11 and Diaz, et al. 21 .
The deposition flux is calculated using a critical shear stress for deposition for each sediment class following the law of Krone 11,21,41,50 . Sediment sliding along the slope is taken into account to prevent an excessive increase of bed slope between depositing banks and the eroding channel. This process is computed by assigning a part of the deposition flux from one cell to the neighbouring one based on the slope between the two cells. The fraction of fresh deposit transposed to a deeper adjacent cell linearly depends on the local slope.
Hindcast simulations over the 2008-2018 period were run through independent years following a morphostatic approach, i.e., no morphodynamic coupling, which is relevant when morphological changes remain relatively small to hydrodynamic processes 15 . This assumption holds for the 2008-2018 period because the Loire Estuary is heavily dredged at a constant depth and no significant changes have been observed in the bathymetry since 2000 9,29 . This is confirmed by the model validation presenting similar skills in 2008 and 2018 (Table 2). Each year was run twice to consider a 1-year spin-up period before analysing the half-hourly outputs 11,16,23 . www.nature.com/scientificdata www.nature.com/scientificdata/ Data records Hindcast repository. The data files containing the results of the Loire Estuary hindcast, i.e., hydrodynamics, temperature, salinity, and sediment dynamics, are available on the CurviLoire Hindcast repository 51 .
• River discharge: • Freshwater: daily-measured runoffs of the Loire and Vilaine rivers (Q L and Q V , respectively); • Sediment load: suspended mud concentration (SMC, in g/l) associated with the river runoff following the following relationships:  www.nature.com/scientificdata www.nature.com/scientificdata/ Salinity. The surface salinity (at 1-m below the surface) is compared at Paimboeuf 'Pa' and Le Pellerin 'LP' stations ( Fig. 1c), within the maximal salinity gradient area. High-frequency (i.e., every 30 minutes) salinity dynamics are well captured by the model along hydrological cycles (Figs. 5b-e, 6b-e). The model underestimates salinity at Le Pellerin in 2008, but the salinity intrusion during the low river discharge period (i.e., from August to November) is well reproduced. In Figs. 5f-I, 6f-i the tide-averaged salinity comparison further illustrates the model's ability to simulate salinity variations at the hydrological and neap-spring time scales with good skills (r 2 ≥ 0.7; Table 2).
Suspended sediment concentration. The surface SSC (at 1-m below the surface) is compared at five stations along the estuary, where the turbidity maximum takes place (i.e., Paimboeuf 'Pa' , Cordemais 'Co' , Le Pellerin 'LP' , and Bellevue 'Be' ; Fig. 1c). The seasonal and neap-spring variability of high-frequency SSC is reasonably well captured by the model at the different stations, but there is a main underestimation of highly-turbid events (Figs. 7, 8). This is especially visible at the downstream stations during summer (i.e., LP, Co, and Pa). Such underestimations are relatively common in the numerical modelling of estuarine sediment dynamics 53 , as monitoring stations along the shore may measure large and local sediment resuspensions that models cannot capture with a 50 to 100 m resolution 21 . However, the model presents better skills at tidal timescales (Table 2), providing confidence in its ability to simulate the main SSC levels along the year (Figs. 9, 10). This is confirmed by the comparison of measured and simulated SSC in function of tidal range and river discharge conditions (Fig. 11). We observe that the model underestimates the SSC at Cordemais and Le Pellerin in 2008 (Fig. 11i,j,m,n), which is not the case in the wetter year 2018 (Fig. 11k,l,o,p). In addition, the model proves to be able to simulate the main tidal and river dynamics.
The model validation of the Loire Estuary hydrodynamics, salinity, and sediment dynamics provides a sufficient level of confidence for using the numerical hindcast in various interdisciplinary studies. However, it is important to acknowledge the model's limitations and errors ( Table 2) to properly use the derived environmental   Fig. 1c). Measurements (blue circles) and simulations (red triangles) from January to December 2008 (two left panels) and from January to December 2018 (two right panels). Symbols represent class-averaged SSC hf values (i.e., every 0.5 m for TR SN and every 250 m 3 /s for Q), and brackets represent standard deviation.